Question

Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be

• A. A circle
• B. An ellipse
• C. A straight line
• D. A parabola

Answer 1

Answer: (C)

A straight line

Answer 2

If $y_{1} = a_{1}\sin\omega t$ and $y_{2} = a_{2}\sin(\omega t + 0) = a_{2}\sin\omega t$

⇒ $\frac{y_{1}^{2}}{a_{1}^{2}} + \frac{y_{2}^{2}}{a_{2}^{2}} - \frac{2y_{1}y_{2}}{a_{1}a_{2}} = 0$⇒ $y_{2} = \frac{a_{2}}{a_{1}}y_{1}$

This is the equation of straight line